Question

When a cathode ray tube is operated at 2912 V, the velocity of electrons is $3.2\times {10}^{7}m{s}^{-1}$, find the velocity of cathode ray, if tube is operated at 5824 V

• A. $2.4\times {10}^{7}m{s}^{-1}$
• B. $4.5\times {10}^{7}m{s}^{-1}$
• C. $2.4\times {10}^{5}m{s}^{-1}$
• D. $2.4\times {10}^{8}m{s}^{-1}$

Answer 1

The correct option is B $4.5\times {10}^{7}m{s}^{-1}$

$\frac{1}{2}m{v}^2=eV\Rightarrow V\sqrt{\frac{2ev}{m}}\Rightarrow v\propto \sqrt{V}\Rightarrow v_2=v_1\sqrt{\frac{v_2}{v_1}}=3.2\times {10}^7\sqrt{\frac{5824}{2912}}=4.5\times {10}^{7}m{s}^{-1}$